oriol pujolàs

Oriol PujolàsIFAE & Universitat Autònoma de Barcelona

Emergent Lorentz Invariance from

Strong Dynamics

II Russian-Spanish Congress

St Petersburg

1/10/13

Based on

arXiv:1305.0011 w/ G. Bednik, S. Sibiryakov

+ work in progress w/ M. Baggioli

Motivation

Can Lorentz Invariance be an accidental symmetry ?

Context: Hořava Gravity

recovery of LI at low energies is the most pressing issue phenomenologically

In this talk,

1) LV:

2) Gravity (mostly) turned offbounds from gravity:MLV≤10

15GeV

dynamical preferred frame ”AETHER” uμ

Poincaré → SO(3)⊗ translations

uμ =MLV (1, 0, 0, 0)timelike vev

Motivation

δcψ ψγ iDiψ δcγ

2rB2 δcH

2 |DiH |2 (CPT even)

Motivation

Observational bounds:|cp −cγ|<10−20 !!

| ce −cγ|<10−15 !


2rB2 δcH

2 |DiH |2

EFT expectation: δc : 1−10−3!!!

FINE TUNING

Collins Perez Sudarsky Urrutia Vucetich ‘04 Iengo Russo Serone

‘09Giudice Strumia Raidal ‘10 Anber Donoghue

‘11

(CPT even)

Challenge: can we achieve naturally ~ 10

-20 suppression?

Motivation

RG & Lorentz Invariance

LI-fixed point is IR-attractive !! Chadha Nielsen’ 83


LI-fixed point is IR-attractive !! Chadha Nielsen’ 83

δc =δc0

[1−β g02log(μ /M)]

β δc

β

g 2 =g02

1− β g02 log(μ /M)

δcψ k

r 2

δcH kr 2

g

@ 1 loop:

E.g., LV – Yukawa theory:

(4π )2d g

dlogμ=β g3


LI-fixed point is IR-attractive !!

E.g., LV – Standar Model (SME)

Giudice Strumia Raidal’ 10


LI


In weakly coupled theories, LI emerges... very slowly!

Suppression is only by a factor

Log ΛUV

ΛIR

⎛

⎝⎜⎞

⎠⎟: 10

LI

LI

let’s accelerate the running by turning to strong coupling


Idea:

δc=μβ*g*

2

(4π )2δc0Near a strongly-coupled fixed point:

accelerated running


Idea:

δc=μβ*g*

2

(4π )2δc0Near a strongly-coupled fixed point:

accelerated running


power > 0 granted ( )

LV deformation

Unitarity bound

=> is an irrelevant coupling

Dim ∂μφ ∂νφ( ) ≥4

βδc > 0

δc

δc ∂tφ∂tφsuggests that ELI should not be an exceptional phenomenon

AdS boundary

AdS

Holography

AdS interior

IR / composite UV / elementaryCFT

RG scale

CFTs at large N and large ‘t Hooft limit geometrize

Toy model #1: LV Randall-Sundrum

Lifshitz / LV boundary condition

AdS

IR UV

Dual to a CFT + UV cutoff (coupling to LV gravity, )

+ IR cutoff (confining, )

LV-Randall-Sundrum

ΛQCD

MP

L =LCFT (OΔ ) −φ w2 −c2k2( )φ +λφOΔ

LV-Randall-Sundrum

RS Realizes a CFT with an operator and a LV sourceOΔ φ

∂5Φ = (w 2 − c2k2 )Φ

probe scalar with LV boundary

W5−M2( )Φ =0

Bednik OP Sibiryakov ‘13

L =LCFT (OΔ ) −φ w2 −c2k2( )φ +λφOΔ

LV-Randall-Sundrum

RS Realizes a CFT with an operator and a LV sourceOΔ φ

if relevant (Δ< 3)

=> Emergent LI

λ


wi2 (k2 ) ; mi

2 + (1+δci2)k2 +

k2+2n

M(i, n)2n∑

LV-Randall-Sundrum

δci

2 :δcUV

2

λ 2ΛIR

ΛUV

⎛

⎝⎜⎞

⎠⎟

2(3−Δ)

Dispersion relations of bound-states: Bednik OP Sibiryakov ‘13

(Optimal case, Δ=2)

power-law suppressed!for relevant couplings (Δ < 3 )

wi2 (k2 ) ; mi

2 + (1+δci2)k2 +

k2+2n

M(i, n)2n∑

LV-Randall-Sundrum

δci

2 :δcUV

2

λ 2ΛIR

ΛUV

⎛

⎝⎜⎞

⎠⎟

2(3−Δ)

power-law suppressed!for relevant couplings (Δ < 3 )


(Optimal case, Δ=2)

Dispersion relations of bound-states:

Toy model #2: Lifshitz flows

Lifshitz Holography

ds2 =

l 2

r2 dr2 +r2

l 2 drx2−

r 2 z

l 2zdt2

Kachru Liu Mulligan ‘08

z >1

Lifshitz solutions in Einstein + Proca + Λ :

z=1

z = d-1

m2L2

At ∝ r z

ds2 =g(r)

l 2

r2 dr2 +r2

l 2 drx2− f(r)

r 2 z

l 2zdt2

Lifshitz Holography

AdS LifshitzLifshitz

At

AdS

log(r)

δGφ (w, k)

−1 ; (p2 )Δ−2 1+ w2 (p2 )(Δ1 −5)

Λ*2(Δ1−4)

+(p2 )(Δ−2)

Λ*2(Δ−1)

+ ...⎛

⎝⎜⎞

⎠⎟+ ...

⎡

⎣⎢

⎤

⎦⎥

The flow imprints modified scaling into the scalar propagator

Qualitative agreement with Gubser ‘time warp’ geometries

Bednik OP Sibiryakov ’13

Lifshitz Holography

Gubser ‘08

δGφ (w, k)

−1 ; (p2 )Δ−2 1+ w2 (p2 )(Δ1 −5)

Λ*2(Δ1−4)

+(p2 )(Δ−2)

Λ*2(Δ−1)

+ ...⎛

⎝⎜⎞

⎠⎟+ ...

⎡

⎣⎢

⎤

⎦⎥


δc2 ;

(ΛIRLUV )2(Δ1 −4)

(ΛIRLUV )2(3−Δ)

⎧⎨⎪

⎩⎪

... and into the dispersion relations of bound states


Lifshitz Holography

δGφ (w, k)

−1 ; (p2 )Δ−2 1+ w2 (p2 )(Δ1 −5)

Λ*2(Δ1−4)

+(p2 )(Δ−2)

Λ*2(Δ−1)

+ ...⎛

⎝⎜⎞

⎠⎟+ ...

⎡

⎣⎢

⎤

⎦⎥


δc2 ;


(ΛIRLUV )2(3−Δ)

⎧⎨⎪

⎩⎪


In the simplest model – not very large suppression Δ1 ≤ 4.35


Lifshitz Holography

δGφ (w, k)

−1 ; (p2 )Δ−2 1+ w2 (p2 )(Δ1 −5)

Λ*2(Δ1−4)

+(p2 )(Δ−2)

Λ*2(Δ−1)

+ ...⎛

⎝⎜⎞

⎠⎟+ ...

⎡

⎣⎢

⎤

⎦⎥


δc2 ;


(ΛIRLUV )2(3−Δ)

⎧⎨⎪

⎩⎪


In the simplest model – not very large suppression Δ1 ≤ 4.35


Lifshitz Holography

can be made arbitrarily large w/ non-minimal couplings Baggioli & OP in progress

Conclusions

RG + Strong Dynamics => fast Emergence of LI

Emergent LI may not be an exceptional phenomenon

The leading LV corrections are characterized by an exponent

determined by the LILVO – least irrelevant LV operator

-> RG scale = compositeness scale

-> how large can be ??

δc : ΛIR

ΛUV

⎛

⎝⎜⎞

⎠⎟

ΔLILVO − 4

ΔLILVO

compositeness – at low Energies ~ 100 TeVmore strongly tested species -> more composite

Limits on compositeness in SM? Λ ≥10 −100 TeV

Discussion

Realizing a composite SM? – no problem with fermions & H

Possible embedding of SM in a NR setup consists of SM=low-lying composite states of a strong sector

Several QFT-mechanisms for Emergence of LI exist

Via naturalness, NRQG becomes very predictive: new physics at much lower energies

Discussion

Non Relativistic SUSY – Groot-Nibelink Pospelov ‘04

Large N species (extra dim) – Anber & Donoghue ‘11

Separation of scales – Pospelov & Shang ‘10

105 GeV

New physics

1015 GeV

NR physics

Thank you!

oriol pujolàs

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